Stationary covariances associated with exponentially convex functions

Exponentially Convex Functions on Hypercomplex Systems

Higher order close-to-convex functions associated with Attiya-Srivastava operator

In this paper‎, ‎we introduce a new class$T_{k}^{s,a}[A,B,alpha‎ ,‎beta ]$ of analytic functions by using a‎ ‎newly defined convolution operator‎. ‎This class contains many known classes of‎ ‎analytic and univalent functions as special cases‎. ‎We derived some‎ ‎interesting results including inclusion relationships‎, ‎a radius problem and‎ ‎sharp coefficient bound for this class‎.

Growth Rates of Sample Covariances of Stationary Symmetric -stable Processes Associated with Null Recurrent Markov Chains

A null recurrent Markov chain is associated with a stationary mixing SS process. The resulting process exhibits such strong dependence that its sample covariance grows at a surprising rate which is slower than one would expect based on the fatness of the marginal distribution tails. An additional feature of the process is that the sample autocorrelations converge to non-random limits.

higher order close-to-convex functions associated with attiya-srivastava operator

in this paper‎, ‎we introduce a new class$t_{k}^{s,a}[a,b,alpha‎ ,‎beta ]$ of analytic functions by using a‎ ‎newly defined convolution operator‎. ‎this class contains many known classes of‎ ‎analytic and univalent functions as special cases‎. ‎we derived some‎ ‎interesting results including inclusion relationships‎, ‎a radius problem and‎ ‎sharp coefficient bound for this class‎.

Complexity of finding near-stationary points of convex functions stochastically

In the recent paper [3], it was shown that the stochastic subgradient method applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate O(k−1/4). In this supplementary note, we present a stochastic subgradient method for minimizing a convex function, with the improved rate Õ(k−1/2).